GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 05 Dec 2019, 11:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 474
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

02 Nov 2013, 00:47
1
7
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:26) correct 39% (01:30) wrong based on 273 sessions

### HideShow timer Statistics

If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3

(2) x - y = 3

GH-06.05.13 | OE to follow
Intern
Joined: 14 Aug 2013
Posts: 31
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE: Consulting (Consumer Electronics)
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

02 Nov 2013, 01:36
1
1
avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3

(2) x - y = 3

GH-06.05.13 | OE to follow

From Stmt 1) y=3,then x^2-9=27=> x^2=36
=>x=6 or -6
then (x+y)^2 will be (6+3)^2=81 or (-6+3)^2=9
Hence not sufficient

From Stmt 2) (x-y)=3 and x^2-Y^2=27
=>(x-y)(x+y)=27
=>(x+y)=9
=>(x+y)^2=81
Hence Stmt 2 alone is Sufficient
Ans B
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4121
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

Updated on: 02 Sep 2019, 07:24
1
Top Contributor
avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3
(2) x - y = 3

Target question: What is the value of (x+y)²?

Given: x² - y² = 27

Statement 1: y = 3
Take x² - y² = 27 and replace y with 3 to get: x² - (3)² = 27
Evaluate: x² - 9 = 27
Simplify: x² = 36
So, EITHER x = 6 OR x = -6
Let's test each case:
Case a: x = 6 and y = 3. So, (x + y)² = (6 + 3)² = 9² = 81. So, in this case, the answer to the target question is (x+y)² = 81
Case b: x = -6 and y = 3. So, (x + y)² = (-6 + 3)² = (-3)² = 9. So, in this case, the answer to the target question is (x+y)² = 9
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y = 3
Take x² - y² = 27 and FACTOR the left side to get: (x + y)(x - y) = 27
Replace (x-y) with 3 to get: (x + y)(3) = 27
So, it must be the case that (x+y) = 9
If (x+y) = 9, then (x+y)² = 81
So, the answer to the target question is (x+y)² = 81
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 24 Jan 2018, 15:40.
Last edited by GMATPrepNow on 02 Sep 2019, 07:24, edited 1 time in total.
Intern
Joined: 02 Aug 2019
Posts: 4
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

01 Sep 2019, 05:29
1
GMATPrepNow wrote:
avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3
(2) x - y = 3

Target question: What is the value of (x+y)²?

Given: x² - y² = 27

Statement 1: y = 3
Take x² - y² = 27 and replace y with 3 to get: x² - (3)² = 27
Evaluate: x² - 9 = 27
Simplify: x² = 18
So, EITHER x = √18 OR x = -√18
Let's test each case:
Case a: x = √18 and y = 3. So, (x + y)² = (√18 + 3)². So, in this case, the answer to the target question is (√18 + 3)²
Case b: x = -√18 and y = 3. So, (x + y)² = (-√18 + 3)². So, in this case, the answer to the target question is (-√18 + 3)²
NOTE: We need not actually calculate the values of (√18 + 3)² and (-√18 + 3)². We need only see that the two values are DIFFERENT
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y = 3
Take x² - y² = 27 and FACTOR the left side to get: (x + y)(x - y) = 27
Replace (x-y) with 3 to get: (x + y)(3) = 27
So, it must be the case that (x+y) = 9
If (x+y) = 9, then (x+y)² = 81
So, the answer to the target question is 81
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

Posted from my mobile device
Intern
Joined: 21 May 2016
Posts: 1
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

01 Sep 2019, 05:47
1
the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.

Posted from my mobile device
Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 474
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

05 Nov 2013, 22:42
Official Explanation

- First, recognize that x^2 - y^2 = (x + y)(x - y). That makes the expression a little more similar to what we're looking for -- both this and (x + y)^2 contain a (x + y) term.

Statement (1) is insufficient. If y = 3, then x^2 - 9 = 27, so x^2 = 36. x must be either 6 or -6. If x = 6, the answer is (6 + 3)^2 = 81, but if x = -6, the answer is (-6 + 3)^2 = 9.

Statement (2) is sufficient. Since (x + y)(x - y) = 27, if (x - y) = 3, then (x + y) = 9. We're looking for (x + y)^2, which is 9^2 = 81. Choice (B) is correct.
Retired Moderator
Joined: 22 Aug 2013
Posts: 1415
Location: India
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

02 Dec 2017, 01:04
avohden wrote:
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?

(1) y = 3

(2) x - y = 3

GH-06.05.13 | OE to follow

x^2 - y^2 = 27 OR (x+y)(x-y) = 27
We need to find (x+y)^2, for which we need (x+y). Here various cases are possible for (x+y) and (x-y).. Eg, former could be 9 and latter 3 or former could be 3 and latter 9 or former could be -3 and latter -9.

(1) y=3. Substituting this we get
x^2 - 3^2 = 27 OR x^2 = 27+9=36. Two values are possible for x here: 6 and -6, this will give two different answers for x+y. So Insufficient

(2) x-y=3. Substituting this we get
(x+y)*3 = 27 or x+y =9. So we can get (x+y)^2. Sufficient.

GMAT Tutor
Joined: 17 Sep 2014
Posts: 281
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

01 Sep 2019, 12:59
Analyzing the question:
To figure out $$(x + y)^2$$ we only need $$x + y.$$ Since we are given $$x^2 - y^2 = (x - y)(x + y) = 27$$, knowing $$x - y$$ would also give $$x + y$$ from that equation. Therefore we are trying to find $$x - y$$, $$x + y$$, or both values of x and y.

Statement 1:
(1) This gives us $$x^2 = 36$$ but we don’t know if x is positive or negative. The two solutions give different values of $$(x + y)^2$$ so this is insufficient.

Statement 2:
(2) As stated above this is sufficient.

_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4121
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?  [#permalink]

### Show Tags

02 Sep 2019, 07:24
Top Contributor
ankitiofs wrote:
the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.

Posted from my mobile device

I have edited my response accordingly.

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Re: If x^2 - y^2 = 27, what is the value of (x + y)^2 ?   [#permalink] 02 Sep 2019, 07:24
Display posts from previous: Sort by